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17.122:
From the result of Problem 17.121, the heat current through each of the jackets
is related to the temperature difference by
(
29
,
ln
2
T
H
a
b
πlk
∆
=
where
l
is the length of the
cylinder and
b
and
a
are the inner and outer radii of the cylinder. Let the temperature
across the cork be
1
T
∆
and the temperature across the styrofoam be
,
2
T
∆
with similar
notation for the thermal conductivities and heat currents. Then,
=
∆
=
∆
+
∆
T
T
T
2
1
.
C
125
°
Setting
H
H
H
=
=
2
1
and canceling the common factors,
1.5
1n
2
1n
2
2
1
1
k

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**Unformatted text preview: **T k T ∆ = ∆ Eliminating gives for solving and 1 2 T T ∆ ∆ . 2 ln 1.5 ln 1 1 2 1 1- + ∆ = ∆ k k T T Substitution of numerical values gives , C 37 1 ° = ∆ T and the temperature at the radius where the layers meet is C. 103 C 37 C 140 ° = °-° b) Substitution of this value for 1 T ∆ into the above expression for H H = 1 gives ( 29 ( 29 ( 29 W. 27 C 37 2 ln K mol J 04 . m 00 . 2 2 = ° ⋅ = π H...

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